If the function $f(x)$ defined by $f(x) = \begin{cases} ax + 1 & \text{if } x \leq 3 \\ bx + 3 & \text{if } x > 3 \end{cases}$ is continuous at $x = 3$, then $(a - b) = ..........$

If $f(x) = \frac{\log_{\sin |x|} \cos^3 x}{\log_{\sin |3x|} \cos^3 (x/2)}$ for $|x| < \frac{\pi}{3}, x \neq 0$ and $f(0) = 4$,then the number of points of discontinuity of $f$ in $\left( -\frac{\pi}{3}, \frac{\pi}{3} \right)$ is:

Prove that every rational function is continuous at every point in its domain.

If the function $f(x) = \begin{cases} \frac{\sqrt{1+px}-\sqrt{1-px}}{x}, & \text{if } -1 \leq x < 0 \\ \frac{2x+1}{x-2}, & \text{if } 0 \leq x \leq 1 \end{cases}$ is continuous in the interval $[-1, 1]$,then $p = $

If $f(x) = |x - 2|$,then

If $f(x) = \begin{cases} \frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & -1 \leq x < 0 \\ 2x^2+3x-2, & 0 \leq x \leq 1 \end{cases}$ is continuous at $x = 0$, then $k$ is equal to